Question

2. An equity portfolio manager rarely if fully invested in the fund but will have some funds in cash. Unfortunate, this creates what is called a cash drag on the portfolio due to the low return on cash funds. On way to deal with this is called neutralizing cash. It involves using stock index futures to synthetically raise the equity position of the portfolio to overcome the cash drag. The portfolio currently has an asset value of $500 million. 95% of it is invested in a stock portfolio that has an average beta=1.0. The reaming 5% is in a cash fun. In a six month period the broad market (s&p) rise by 11.50% while the cash fund rises by 2.5%.

a. Based on the portfolio weight, compute the portfolio weight average over the six month period. Compare this return to the board market return. How much did the portfolio underperform  the market?

b. One way to add return is to synthetically add stock exposure with stock index futures. We want to have a synthetically portfolio that has 100% stock exposure so we need to add 5% of the portfolio value in stock index future? The current index future price is 1200 and the contract size is $250 times the index. This is different than hedge in that we want the additional stock exposure so we would take a long position inn future. The chosen contract will mature three months from today?

c. In three months the following changes have taken place: The S&P 5 has gone from 1120 to 1220 and the contract matures so convergence taken place. Based on portfolio these parameters, analyze the performance of the futures position. How much portfolio value did the extra equity exposure add?

Answer 1

Part (a)

Beta of the stock portfolio = B_SP = 1.0

Market return in 6 months, R_M = 11.50%

Return on the stock portfolio, R_SP = B_SP x R_M = 1 x 11.50% = 11.50%

Return on cash, R_C = 2.5%

Portfolio's weight average return in six months = Proportion of investment in stock portfolio x R_SP + Proportion of investment in cash x R_C = 95% x 11.50% + 5% x 2.5% = 11.05%

So, the portfolio under performed by 11.50% - 11.05% = 0.45% with respect to the broad market (represent by S&P)

Part (b)

Amount available for buying future contracts = 5% of portfolio = 5% x $ 500 mn = $ 25 mn

Current index future = 1,200

Multiplier = 250

Number of future contracts to be bought = 25,000,000 / (250 x 1,200) = 83.33 contracts or say 83 contracts (integral number)

Part (c)

Return on the long position in futures in three months = Future price after three months - Future price initially

Since there is a convergence between spot and future at the end of three months,

Future price after three months = Spot price after three months = 1220

Hence, Return on the long position in futures in three months = Future price after three months - Future price initially = 1,220 - 1,200 = 20

So, portfolio value added by the futures = total gain due to futures = Nos. of contracts x Multiplier x Gain in future price = 83 x 250 x 20 = $ 415,000